I agree that 'guten Beziehungen' misses the point, though I would support adding some other translation for numbers person (/ man / woman) if it could be agreed on.
The explanation in the last paragraph of #1 is generally good. A numbers person is a person who specializes in or enjoys working with numbers, in the sense of figures: that is, math, statistics, accounting, budgeting, economics, data analysis, any kind of analysis that is more quantitative than qualitative. In the Time article, as CM2DD suggests, it may refer less to inherent traits than to the role he has assumed within the legislature and his party: the person who has focused on the numbers, on the bottom line, perhaps not only in regard to budget planning but also vote counting, state-by-state electoral strategy.
OT: All that said, 'numbers man' is probably more a convenient shorthand than an accurate description of his complete character, as he seems equally interested or more so in social issues, where his views are fervently ideological. ('Opus Dei man' might be closer to the truth -- would be nice if some enterprising reporter could find out.)